The structure of the tensor product of 𝔽 2 [-] with a finite functor between 𝔽 2 -vector spaces
Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805.

Soit la catégorie de foncteurs de la catégorie des 𝔽 2 -espaces vectoriels de dimension finie dans la catégorie des 𝔽 2 -espaces vectoriels. Nous étudions la structure du foncteur IF, où F est un foncteur fini et I désigne le foncteur injectif V𝔽 2 V * . Un théorème de détection de sous-foncteurs de IF est démontré, ce qui est la base de la démonstration que le foncteur IF est artinien de type un.

The paper studies the structure of functors IF in the category of functors from finite dimensional 𝔽 2 -vector spaces to 𝔽 2 -vector spaces, where F is a finite functor and I is the injective functor V𝔽 2 V * . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors IF are artinian of type one.

@article{AIF_2000__50_3_781_0,
     author = {Powell, Geoffrey M. L.},
     title = {The structure of the tensor product of ${\mathbb {F}}\_2[-]$ with a finite functor between ${\mathbb {F}}\_2$-vector spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {781--805},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {3},
     year = {2000},
     doi = {10.5802/aif.1773},
     mrnumber = {2001h:20065},
     zbl = {0958.18006},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2000__50_3_781_0/}
}
Powell, Geoffrey M. L. The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces. Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805. doi : 10.5802/aif.1773. https://aif.centre-mersenne.org/item/AIF_2000__50_3_781_0/

[J] G.D. James, The representation theory of the symmetric groups, Lecture Notes in Math., 682 (1978). | MR 80g:20019 | Zbl 0393.20009

[J2] G.D. James, The decomposition of tensors over finite fields of prime characteristic, Math. Zeit., 172 (1980), 161-178. | | MR 81h:20015 | Zbl 0438.20008

[JK] G.D. James, A. Kerber, The Representation Theory of the Symmetric Groups, Ency. Math. Appl., Addison-Wesley, Vol. 16, 1981. | MR 83k:20003 | Zbl 0491.20010

[K1] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : I, Amer. J. Math., 116 (1993), 327-360. | MR 95c:55022 | Zbl 0813.20049

[K2] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : II, K-Theory, 8 (1994), 395-426. | MR 95k:55038 | Zbl 0830.20065

[K3] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : III, K-Theory, 9 (1995), 273-303. | MR 97c:55026 | Zbl 0831.20057

[PS] L. Piriou, L. Schwartz, Extensions de foncteurs simples, K-theory, 15 (1998), 269-291. | MR 2000g:20085 | Zbl 0918.20036

[P1] G.M.L. Powell, with an Appendix by L. SCHWARTZ, The Artinian conjecture for I ⊗ I, J. Pure Appl. Alg., 128 (1998), 291-310. | Zbl 0928.18004

[P2] G.M.L. Powell, Polynomial filtrations and Lannes' T-functor, K-Theory, 13 (1998), 279-304. | MR 99c:55016 | Zbl 0892.55009

[P3] G.M.L. Powell, The structure of Ī⊗Λn in generic representation theory, J. Alg., 194 (1997), 455-466. | MR 98g:55020 | Zbl 0893.55011

[P4] G.M.L. Powell, The structure of the indecomposable injectives in generic representation theory, Trans. Amer. Math. Soc., 350 (1998), 4167-4193. | MR 98m:18004 | Zbl 0903.18006

[P5] G.M.L. Powell, On artinian objects in the category of functors between ℙ2-vector spaces, to appear in Proceedings of Euroconference 'Infinite Length Modules', Bielefeld, 1998. | Zbl 1160.18305